Solid Solution?

Me and my classmate were thinking of questions the other could not answer. This was what I came up with.

If   $^c\sqrt {a^c\over b^a} = ^d\sqrt{b^d\over a^b}$and abcd=100, then what is a+b+c+d=?

I know the answer is 14 or 22(2 possible answers but im not sure of them) but I need a solid solution

(PS: i dont know how to put c and d as the index of a radical. Dont judge.)